Problem Statement

Given is a directed tree with $N$ vertices numbered $1$ through $N$.

Vertex $1$ is the root of the tree. For each integer $i$ such that $2 \leq i \leq N$, there is a directed edge from Vertex $p_i$ to $i$.

Let $a$ be the permutation of $(1, \ldots, N)$, and $a_i$ be the $i$-th element of $a$.

Among the $N!$ sequences that can be $a$, find the number of sequences that satisfy the following condition, modulo $998244353$.

• Condition: For every integer $i$ such that $1 \leq i \leq N$, Vertex $i$ is unreachable from Vertex $a_i$ by traversing one or more edges.

Constraints

• All values in input are integers.
• $1 \leq N \leq 2000$
• $1 \leq p_i < i$

Input

Input is given from Standard Input in the following format:

N
p_{2} \cdots p_N

Output

Print the number of sequences $a$ among the permutations of $(1, \ldots, N)$ that satisfy the condition in Problem Statement, modulo $998244353$.